Does Vex Apathetic target?

No, Vex, Apathetic does not target.

According to Rule 355.10.d, a game object is not a target if it is "programmatically selected based on its characteristics rather than chosen by the spell or ability’s controller."

When an opponent plays a unit, Vex's ability automatically identifies and selects that specific unit based on the trigger condition ("When an opponent plays a unit"). Because the ability does not require you to make a choice or designate a target, it bypasses protection abilities that prevent a unit from being "chosen" by enemy spells or abilities (such as those found on units like Baron Nashor or Ruin Runner).

This is supported by RiftJudge FAQ #8685 and RiftJudge FAQ #8772, which clarify that programmatic selection is distinct from targeting.